please help me i dont know this

Please Help Me I Dont Know This

Answers

Answer 1

When the coin is tossed and then dice is rolled, the possible outcomes are 12.

Define the term sample space/possible outcome?All potential results make up as sample space of such a random experiment.A subset of such sample space is an event connected to a random experiment.Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.The total likelihood of all outcomes in an event A is the probability of that event.

For the stated question.

Sample space for tossing coin. { H, T}.

Sample space for rolling dice. { 1, 2, 3, 4, 5, 6 }

Then,

Total sample = { H1, H2, H3,H4, H5, H6, T1, T2, T3, T4, T5, T6}

Thus, the total possible outcomes for tossing coin and rolling dice is 12.

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Anyone know this? Struggling highschool student here

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The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.

Calculate the monthly payment?The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.To calculate this, first you must review the Monthly Principal & Interest Factor chart.Since the credit score is 711, this falls into the range of 710-729. For a 15-year term, the interest factor is 7.0.Once you have determined the interest factor, you can then calculate the monthly payment.To do this, you must subtract the 15% down payment of $47,280.00 from the purchase price of $315,200.00, which leaves $267,920.00.Then, you must multiply the $267,920.00 by the interest factor of 7.0 and divide it by 12 to get the monthly payment of $2,408.60.

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What number would you multiply the second equation by in order to eliminate the x term when adding to the first equation?.

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In order for the variables in the first equation to cancel out, we must multiply a number in the second equation to make it equal to those variables. For instance, we must multiply the second equation by two in order to make it equal four in order to cancel out x.

To make the variables in the first equation cancel each other out, we must multiply a number in the second equation to make it equal to those variables. For instance, we must multiply the second equation by two in order to make it equal four in order to cancel out x. We must now multiply the second equation by 3 in order to equal 9y in order to eliminate y.

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B is the midpoint of AC. AB - 6x + 1 and BC - 2x + 9. Find the length of AC

Answers

The length of AC in the line segment is 26 units.

How to find the length of a line segment?

B is the midpoint of AC.  

AB = 6x + 1

BC = 2x + 9

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

Hence,

AB = BC

6x + 1 = 2x + 9

6x - 2x = 9 - 1

4x = 8

divide both sides by 4

x = 8 / 4

x = 2

Therefore,

AC = 2AB

AC = 2(6x + 1)

AC = 2(6(2) + 1)

AC = 2(12 + 1)

AC = 26 units

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What is the area of a triangle whose height is 6 cm and base is 10 cm?.

Answers

The area of a triangle whose height is 6 cm and the base is 10 cm is 30 cm².

Area of triangle = 1/2 × b × h

= 1/2 × 10 × 6

= 1/2 × 60

= 30 cm².

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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What kind of line is Y =- 6?.

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y = -6 is a horizontal line and perpendicular to y-axis.

A horizontal line is perpendicular to the y-axis and parallel to the x-axis.

The equation for a horizontal line is y = c.

where c is constant and c constant is the y-coordinate of every point on the line.

In the equation y = -6, the constant is -6.

This means that every point on this line has an y-coordinate of -6.

Every point on the line (x, y) will have a y-coordinate of -6, while the

x-coordinate can be anything.

Therefore, y = -6 represent a horizontal straight line with perpendicular to the y-axis and parallel to the x-axis.

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write the trinomial as a square of a binomial or as an expression opposite to a square of a binomial
24ab-16a^2-9b^2

Answers

-(4a-3b)^2 is the answer

Answer: The given trinomial, 24ab-16a^2-9b^2, can be written as an expression opposite to a square of a binomial.

To do this, we first factor out the greatest common factor of -4a, which gives us:

-4a(6b-4a-9b^2)

We can then factor -9b^2 as -(3b)^2, and group the remaining terms together:

-4a((3b-2a)^2-4a^2)

So the trinomial can be written as -4a( (3b-2a)^2 - 4a^2 ) which is an expression opposite to a square of a binomial (3b-2a)^2.

Step-by-step explanation:

What is the range of this radical function f(x) =4squareroot x-6

Answers

Answer: Unless there is a vertical shift the range for ALL radical functions will remain [0,infinity)

Step-by-step explanation:

Please Help. The picture of the question is below. My teacher is going to fail me if I do not get this question so please make it snappy.

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The roots of a function are the points at which the graph of the function crosses the x-axis.

What are the roots of the function?The definite solutions to the equation are x = -2 and x = 1.The equation for the function whose graph is shown is y = (x+2)(x-1).The roots of the function are x = -2 and x = 1.The definite solutions to the equation are x = -1 and x = 3.The equation for the function whose graph is shown is y = (x + 1)^2 - 4.The roots of the function are x = -1 and x = 3.These are the x-coordinates of the points where the graph crosses the x-axis.They are also the solutions to the equation y = 0.The roots are also known as the zeros of the function. In other words, the roots of a function are the values of x that make the function equal to zero.For example, the equation x^2 + 3x + 2 = 0 has roots at x = -1 and x = -2. This means that when x is equal to -1 or -2, the equation's left-hand side (x2 + 3x + 2) is equal to zero.

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There were 200 members at a skating club. Membership dropped by 30%. How many members are there now?

Answers

Answer:

140 members

Step-by-step explanation:

find 70% of 200

Is the solution set the answer?.

Answers

Any value of a variable that makes the equation true is a solution. The set of all variables that makes the equation true is called a solution set. Because 2(4) + 6 = 14, the solution set for 2y + 6 = 14 is 4.

How do I locate the set of solutions?

Plugging each value in the domain into the equation to obtain the range values is the first step in determining the solution set for an equation with a given domain. Write these values as a set and create ordered pairs from them. Your response is that set!

Is the math answer the solution?

An assignment of values to the unknown variables that achieves equality in the equation is called a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used in place of the unknowns, makes the equation equal.

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Full Question = How do you find the solution set of an equation?

What i the difference between 4 x 3 and 43? Prove your anwer and explain your thinking

Answers

The difference between 4 x 3 and 43 is that 4 x 3 is the mathematical operation of multiplying 4 and 3, which equals 12, while 43 is just a number.

The Mathematical Operations

The difference between the expression "4 times 3" and the number 43 is that the former indicates the mathematical action of multiplying "4 times 3," which results in the value 12, while the latter simply represents the number itself.

To prove this, you can perform the mathematical operation of 4 x 3 = 12 and compare it to the number 43. As 12 is not equal to 43, it is clear that these are two different values.

In general, when we see a number with multiple digits, like 43, it is generally not thought of as the result of a mathematical operation. However, when we see an expression like 4 x 3, we know that it is the result of a multiplication operation and it is not just a number.

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What is the largest integer value that makes this inequality true?
4x-8<-2x+1

Answers

Answer:

Step-by-step explanation:

the answer would be 10

What is the modulus of the complex number 4 +3i?.

Answers

The modulus of the complex number is:

|z| = 5

Now, According to the question:

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

The modulus of complex number  z=a+bi  is:

[tex]|z| = \sqrt{(a+bi)(a-bi)}[/tex]

[tex]|z| = \sqrt{a^2+b^2}[/tex]

The given complex number is :

4 + 3i.

a = 4 and b = 3

The modulus of the complex number will be:

[tex]|z|=\sqrt{4^2+3^2}[/tex]

[tex]|z|=\sqrt{16+9}\\\\|z|=\sqrt{25}[/tex]

|z| = 5

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A comedy club earns $1088 from an opening night performance and $1183 from a second performance

Answers

The solution is $95.

What is Subtraction?

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

A comedy club earns $1088 from an opening night performance

and $1183 from a second performance

so, earns more =$(1183-1088)

                         =$95

Hence, the solution is $95.

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the cost of chesse increased by 25%. how much is the new price of the cheese that originally cost $4.20. PLEASE HELP WILL GIVE BRAINLIST FOR SOLULTIONS

Answers

Answer:

Step-by-step explanation: The answer is $48.15 hopes this helps :)

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K is the midpoint of GJ and H is the midpoint of GI
If IJ =z-4 and HK = z - 37, what is the value of z?

Answers

The value of z from the triangle is z = 70

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔIGJ

Let the second triangle be represented as ΔHGK

Now , K is the midpoint of GJ and H is the midpoint of GI

So , IH = GH and GK = KJ

And , the triangles ΔIGJ and ΔHGK are similar

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

The measure of HK = ( 1/2 ) measure of side IJ

And , ( z - 37 ) = ( 1/2 ) x ( z - 4 )

On simplifying the equation , we get

Multiply by 2 on both sides of the equation , we get

2z - 74 = z - 4

Subtracting z on both sides of the equation , we get

z - 74 = -4

Adding 74 on both sides of the equation , we get

z = 70

Hence , the value of z is 70

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An ad for an exercise product stated: "using this product will burn 74% more calories." What is misleading about this statement

Answers

Answer:

The statement is misleading as it does not provide any context for the comparison. It does not clarify what the 74% more calories is being compared to or what amount of calories is being burned by using the product. Additionally, the advertisement does not provide any evidence to back up the claim.

What are characteristics of perpendicular lines?.

Answers

The characteristics of perpendicular lines:

1) Perpendicular lines are intersecting lines.

2) The perpendicular lines are coplanar.

3) The perpendicular intersect at a 90° angle.

4) The product of slopes of perpendicular lines is -1.

We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°

Since these lines are inclined at 90° to each other, hence they create right angles.

Perpendicular lines are intersecting lines.

Also, the perpendicular lines are coplanar.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

If two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.

The product of slopes of perpendicular lines is always -1.

Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are perpendicular to each other then m₁ × m2₂ = -1

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Five cups of flour are divided equally into 4 bowls. How much flour is in each bowl?

Answers

Answer: D, 1 1/4 cups of flour and 5/4.

Step-by-step explanation:

There are four bowls, so subtract four from 5, and you have 1. Divide the remaining 1 by 4, and you have 1/4. So, 1 1/4 cups per bowl. A simpler way would be to divide 5 by 4, as you would end up with 1.25, which equals 1 1/4.

Answer: 5/4 cups of flower

5 ÷ 4= 1.25

1.25 in fraction form is 5/4, so the answer would be a.

Write a poitive or negative integer that repreent the ituation. You walk up 83 tair

Answers

83 is a positive integer that represents the situation.

An integer is a whole number, meaning it does not include any fractional or decimal component. It can be positive, negative, or zero. Integers are numbers that can be written without a fractional or decimal component.

The number of stairs walked up is a positive value, because it is a quantity that increases, and in mathematics, positive numbers represent an increase in value. In this case, walking up 83 stairs is an increase in elevation, and so it is represented by a positive number.

Therefore, the situation can be written as a positive integer which is 83.

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2.Find the GCF(224,264) using Euclid division algorithm. ​

Answers

Answer:

GCF = 8.

Step-by-step explanation:

First, we divide 264 by 224 and we get the identity:

264 = 1*224 + 40  ( That is 264 divided by 224 goes once and the remainder is 40)

Now we divide 224 by 40 to get:

224 = 5*40 + 24

Repeating this process, we get:

40 = 1*24 + 16

24 = 1*16 + 8

16 = 2*8 + 0   <------ we stop because the remainder is 0.

So, The GCF is 8.

What is the main difference between polynomial and equation?.

Answers

A polynomial is described as a set of mathematical phrases with numerical coefficients, variables, and operations between them. The variables' degree must be a non-negative integer (addition, subtraction, multiplication and division).

A polynomial example could be-

[tex]\mathrm{p}(\mathrm{x})=2 x^{3-3(x+y)+7 / 5}[/tex]

A mathematical notion known as an equation is one in which two quantities are equal and are indicated by the symbol "=" in between.

An illustration of an equation is

[tex]3 x-5 y=(7 x+9) / 5[/tex]

In contrast to polynomials, equations have no limits on the coefficients or the powers of the variables.

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A polynomial is described as a set of mathematical phrases with numerical coefficients, variables, and operations between them.

The variables' degree must be a non-negative integer (addition, subtraction, multiplication and division).

A polynomial example could be-

p(x) =³

A mathematical notion known as an equation is one in which two quantities are equal and are indicated by the symbol "=" in between.

An illustration of an equation is

In contrast to polynomials, equations have no limits on the coefficients or the powers of the variables.

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A game includes spinning a spinner with numbers 1–5 and rolling a number cube with numbers 1–6.


What is the probability of spinning an even number and rolling a 5?

Answers

The values of the probability from spinning the spinner and rolling the cube are;

Probability that the spinner lands on an even number = 2/5Probability of rolling a 5 on the number cube = 1/6Pthe joint probability of the spinner landing on an even number and rolling a 5 = 1/15

What is the probalibilty of an evdent?

Probability is a measure of the liklihood that an event will occur. The probability of an event = Number of times the event occurs ÷ Sum of the frequencies of all possible events.

Numbers on the spinner are; 1, 2, 3, 4, and 5

Numbers in the number cube = 1, 2, 3, 4, 5, and 6

The probability of an event = The number of required outcomes ÷ The number of possible outcomes

The possible even numbers on the spinner = 2, and 4

The number of even numbers in the spinner = 2

The number of possible numbers on the spinner = 5

The ratio of the number of even numbers to the number of possible numbers, which is the probability of spinning an even number, therefore is; P(E) = 2/5

The number of 5s on the cube = 1

The number of possible numbers on the cube = 6

The probability of rolling a 5 on the number cube is therefore, p(5) = 1/6

The probability of landing on an even number and rolling a 5, P(E) × P(5) is therefore;

P(E) × P(5) = (2/5) × (1/6) = 2/30 = 1/15

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Answer:

Probability of spinner landing on an even number-2,5

Probability of rolling a 5

on number cube-1,6

Probability of spinner landing on an even number and rolling a 5-1,15

Step-by-step explanation:

bc

ABCD is a cyclic quadilateral in whicj side Ad and BC are produced to meet at E such that AE = BE .Prove that AB// DC

Answers

Answer: To prove that AB is parallel to DC, we can use the following steps:

Draw a diagram of the cyclic quadrilateral ABCD with the point E where sides AD and BC are produced to meet.

Since ABCD is a cyclic quadrilateral, all its interior angles add up to 360 degrees. Therefore, angle A + angle B + angle C + angle D = 360 degrees.

Since AE = BE, we can say that angles A and B are equal (by corresponding angles). Similarly, angles C and D are also equal.

Since angles A and B are equal and angles C and D are also equal, we can say that angle A + angle B = angle C + angle D.

Substituting this into our equation from step 2, we get: angle A + angle B + angle C + angle D = angle A + angle B + angle A + angle B.

Simplifying, we get: 360 = 2(angle A + angle B). This means that angle A + angle B = 180.

Since angle A + angle B = 180, we can say that angle A = angle B and angle C = angle D.

Now we can use the fact that corresponding angles are equal, then angle A = angle C and angle B = angle D.

We know that opposite angles of a parallelogram are equal, so we have proved that AB is parallel to DC.

It's important to note that this proof uses the fact that quadrilateral ABCD is cyclic, which means that the sum of its angles is equal to 360 degrees. It also uses the fact that opposite angles are equal in a parallelogram, and corresponding angles are equal when two lines are parallel.

Step-by-step explanation:

make a the subject of the relation S(a+b) =t​

Answers

Answer:[tex] \sqrt{2x + 3} [/tex]

Answer:

a = [tex]\frac{t-sb}{s}[/tex]

Step-by-step explanation:

s(a + b) = t    Distribute the s

sa + sb = t      Subtract sb from both sides

sa + sb - sb = t - sb  Simplify

sa = t - sb    Divide both sides by s

a = [tex]\frac{t-sb}{s}[/tex]

The area of the quare felid i 40,000 quared and we want to but a fence diagonally through the field. What hould the length of the fence be?

Answers

The length of the fence must be 282.84 ft.

Area of the field =  40,000 ft²,

The length of the fence will be equal to the diagonal of the square.

For a square of side length S, the area is:

A = S²

Substituting the values in the formula -

S² = 40,000 ft

Applying the square root on both sides -

S = √(40,000 ft²)

Calculating, the diagonal of a square of side length S is:

D = S x√2,

Substituting the values -

D = √(40,000 ft²) x √2

= √(80,000 ft²)

= 282.84 ft

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The owner of a bookstore buys used books from customers for $1.50 each.The owner then resells the used books for 400% of the amount he paid for them.What is the price of a used book in this bookstore?

Answers

The selling price of a used book at the store where the owner buys a used book for $1.50 and resells the used book at a price of 400% the price at which buys the used book is $6.00

What is the selling price of a commodity?

The selling price of an item is the price which is displayed on the item on the shelves of a store. The selling price is often different from the price at which the item is bought, or produced, which is often lesser than the price at which the item is sold.

The amount at which the owner buys each used book = $1.50

The amount at which the owner of the used book store sells the books = 400% of the amount he paid for the books

400% of an amount x is equivalent to four times the amount. (4 × x)

The price at which the owner sells a used book at his store, P, is therefore;

P = 400% × $1.50 = 400/100 × $1.50 = $6.00

The price of a used book at the store is $6.0

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How many solutions does the pair of linear equations y 0 and y =- 7 have?.

Answers

The pair of linear equations y = 0 and y = -7 have no solution.

Given the pair of equations is

y = 0

y = -7

We have to find a solution.

Here, b₁ = 1, c₁ = 0

b₂ = 1, c₂ = -7

So, b₁/b₂ = 1/1 = 1

c₁/c₂ = 0/-7 = 0

So, b₁/b₂ ≠ c₁/c₂

We know that,

Let's assume a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, then

i) the given pair of linear equations is inconsistent

ii) the graph will be a pair of parallel lines, so the pair of equations will have no solution.

Therefore, the pair of equations has no solution.

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At Jaylen’s school, students must choose a language, an elective, and a science class. Their options are listed in the table.


Course Offerings

Language

Elective

Science

Chinese

Art

Astronomy

French

Band

Biology

German

Choir

Chemistry

Spanish

Computers

Physics


How many different combinations are possible?

Answers

There are twelve possible combinations:

Chinese Art AstronomyChinese Band BiologyChinese Choir ChemistryChinese Computers PhysicsFrench Art AstronomyFrench Band BiologyFrench Choir ChemistryFrench Computers PhysicsGerman Art AstronomyGerman Band BiologyGerman Choir ChemistryGerman Computers Physics

At Jaylen's school, students have a variety of course offerings from which to choose. They must choose a language, an elective, and a science class. The language options are Chinese, French, German, and Spanish.

With these four language options, four elective options, and four science options, there are twelve possible combinations of courses to choose from.

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What is the latest estimate for the likelihood of one or more M 6. 7 earthquakes in the Bay Area region before the year 2043?.

Answers

A 72 percent is the latest estimate for the likelihood of one or more M 6.7 earthquakes in the Bay Area region before the year 2043.

To estimate the likelihood of future earthquakes, scientists rely on a variety of techniques that help us understand the velocities and magnitudes of past earthquakes. Using the Global Positioning System (GPS) and other land surveys and geological techniques,scientists have determined how much current plate movement, totaling inches per year across the San Francisco Bay region, stresses these individuals. We were able to more accurately measure how well it disperses. Small earthquakes occur more frequently than large ones. There is a 98% chance that an earthquake of magnitude 6.0 or greater will occur before 2043. There is a 72% chance that at least one earthquake of magnitude 6.7 or greater will occur in the San Francisco Bay Area, and a 51% chance that at least one magnitude earthquake will occur. Therefore they concluded that there is a 72% chance (or probability) of at least one earthquake of magnitude 6.7 or greater occurring somewhere in the San Francisco Bay Area before 2043.

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power and volume down buttons simultaneously until the qlink logo appears, at which time you release the power button but continue holding volume down choose the compound below that contains at least one polar covalent bond, but is nonpolar. group of answer choices pocl3 pclbr4 pcl5 po2cl both b and c are nonpolar and contain a polar covalent bond. Design a salary slip for the month of Nov 2022 with information given below. Fixed vs variable ratio- 70:30 Ctc - 18L Basic- 50% Hra- 20% Da - 12% Insurance - 2500 Incentive- 75% target completion Pf 12% Earned leaves - 2 LOP - 4 Carol Gilligan criticized Lawrence Kohlberg's theory, stating that it was biased towards men. Gilligan stated that his theory was derived by only studying men and did not take into account a woman's way of thinking or patterns of behavior. which of the following types of attributes are specifically identified by customers as wants and needs. What is the initial value of the function represented by this graph? 0457 physical therapy rehabilitation centers inpatient near me What is deductive reasoning? Write a narrative essay about overcoming a challenge and wha you learned as result in your own words pre writing ,rough draft, and final draft what can a project manager do to manage changes effectively and encourage project adoption? A. Communicate clearly by being transparent and upfront with their ideasB. Avoid having team members as advocates because they may be too enthusiastic about the project C. Create a sense of ownership and urgency around the project D. Reassure employees that adopting the project will not disrupt their work The American Indian Movement was:A. An activist group that protested the US's treatment of native peopleB. The effort to assimilate and integrate Native Americans to white societyC. The migration of Native Americans to cities in the mid-1900sD. The name of the Native American civil rights movement people may claim to be law-abiding but may still engage in behaviors that are illegal. this behavior is an example of , which refers to the values and standards of behavior that people actually follow. group of answer choices material culture real culture universal culture ideal culture Tina and her friend are picking apples at Newberry Orchard. The apples cost $1.40 per pound. If they pick 2.5 pounds of apples, how much will the apples cost?$ Can you help me with this ?! !! 2. AB is tangent to O at A (not drawn to scale). Find the length of the radius r, to the nearest tenth. (The length from the edge of the circle to B is 4.) Which are the findings of research conducted by Perrin and Siegel (2013) regarding children raised by same-sex couples? HELP ASAP!!!!!!Beginning early in the history of the nation, the two-party system has been standard in the United States. The first two major political parties in the United States were the Federalist Party and the Democratic-Republican Party, which formed shortly after the ratification of the constitution. Determine if each item is MOST associated with the Federalist Party or the Democratic-Republican Party. Federalists Democratic-Republicans Alexander Hamilton Federalists Alexander Hamilton Democratic-Republicans Alexander Hamilton In favor of stronger state governments Federalists In favor of stronger state governments Democratic-Republicans In favor of stronger state governments Thomas Jefferson Federalists Thomas Jefferson Democratic-Republicans Thomas Jefferson In favor of a strong central governmen 1 Write a passionate plea summarizing your support of American imperialism 2 Write a passionate please summarizing your opposition to American imperialism social engineering solutions to health problems are less successful than individual behavior modification Did Buddhism affect culture?.